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We present a three-dimensional (3-D) analysis of scattering losses due to sidewall roughness in rectangular dielectric waveguides valid for any refractive-index contrast and field polarization. The analysis is based on the volume current method and uses array factors to introduce significant mathematical simplifications to better understand the influence of individual waveguide parameters on scattering losses. We show that the typical two-dimensional (2-D) analyses can substantially overestimate scattering losses in small waveguides and that scattering losses exhibit considerable polarization dependence. We produce scattering-loss estimates for a wide variety of waveguides and provide guidelines for design of waveguide cross sections that are less sensitive to sidewall roughness.